Use of Uncertainty Calculation Software as a Didactic Tool to Improve the Knowledge of Chemistry Students in Analytical Method Validation

Calculating analytical uncertainties as a part of method validation is a relevant aspect of field and laboratory practices in instrumental analytical chemistry subjects, which usually require complex algorithms. This work describes the development and didactic use of an automatic and straightforward informatics tool, implemented in an Excel macro, for calculating and interpreting the uncertainty of an analytical method against a reference method on field measurements. The software was initially developed for field testing of low-cost air quality monitoring analytical methods against reference methods, and the present work shows its adaptation to a didactic environment. The uncertainty calculation software was implemented through an Excel macro based on Visual Basic as a graphical user interface. It finds a best-fit line that describes the relation between concentrations determined by the candidate and reference methods. The software generates the analytical validation results (slope and intercept with their respective confidence limits, and expanded uncertainty of a concentration determined by the candidate method), hiding the intermediate functions and calculations. The Excel interface eases uncertainty calculations for undergraduate students, although the background mathematics can be quickly unveiled to students for didactic purposes. This tool has been applied to a laboratory exercise focused on validating experimental results obtained in the measurement of ozone levels in ambient air by passive sampling and spectrophotometric detection. The uncertainty calculation software has proved valuable by providing the student a resource to check the analytical quality of the data generated in the laboratory, while assimilating the fundamentals behind the calculations.


SECTION 1. UNCERTAINTY CALCULATION
The European Guide for the demonstration of equivalence of ambient air monitoring methods considers uncertainty as the sum of the uncertainty due to the variability of measurements between two equal candidate samplers/instruments measuring in parallel (if available) plus the uncertainty due to the lack of fit between the candidate method and the reference analyzer measurements.

Between-samplers/instruments uncertainty
The square of the relative standard uncertainty due to the variability of measurements between samplers/instruments ( ) is calculated from the difference  2  between the measurements of the samplers/instruments measuring in parallel, according to Eq. ( S1): where and are the results of parallel measurements for a single paired data period  ,1  ,2 i, is the number of parallel measurements results and is the average of all the   experimental results.
The relative standard uncertainty between samplers/instruments is the square root of .The relative standard uncertainty as a per cent is obtained by multiplying by  2  100.According to the European Guide mentioned above, the relative standard uncertainty (%) should not exceed 5%.

Comparison with the reference method
Regarding the uncertainty due to the lack of fit between the candidate method and the reference analyzer, it is assumed that the relationship between the measurements obtained by the candidate method (y) and the measurements obtained by the reference analyzer (x) can be described by a linear relation of the form Eq. (S2).

(S2)
The linear correlation was evaluated using the orthogonal regression technique (also known as Deming regression), this being preferable to standard regression since it includes the uncertainty of x-axis values.The square of the sampler/instrument uncertainty ( ) as a function of concentration ( ) was calculated from Eq. (S3): where and b are, respectively, the intercept and the slope of the orthogonal regression,  is the number of parallel measurements results, is the standard uncertainty of  (  ) the reference analyzer (obtained from the analyzer specifications or experimental measurements with two reference analyzers in parallel), and is the sum of the  absolute (Eq.S4) or relative (Eq.S5) residuals resulting from the orthogonal regression. 2

Calculation of the combined uncertainty of candidate method
The square of the field combined standard relative uncertainty (at the  2 , maximum value of the series) is calculated by adding plus (at the maximum value of the series), using Eq. ( S6): 2

Calculation of the expanded uncertainty of candidate method
The relative expanded uncertainty of the sampler/instrument at 95% confidence was then calculated according to Eq. ( S7): where the coverage factor is typically = 2.   The mole amount of ozone that has reacted in a period equals the mole amount of ITS consumed.The latter is measured by the decrease of the reagent's absorbance at 600 nm.
Once the amount of ozone has been calculated, it is related to its concentration in ambient air by applying Fick's law, considering that all the ozone has reached the membrane by diffusion.For this purpose, it is necessary to know the sampling rate of the passive sampler, which takes into account its geometry and the diffusion coefficient of the ozone under the ambient conditions of the measurement.The equation for the calculation of the ambient ozone concentration is: where is ozone concentration (µg m -3 ); is the amount of ozone consumed (µg); S

[𝑂 3 ]
is the sampling rate (m 3 min -1 ) and is the sampling time (min).-A 20 mg L -1 ITS working solution.Dilute the stock standard solution 1/50 with water in a 50 mL flask.It is prepared just before use.

2.2.SAMPLING WITH PASSIVE SAMPLERS
Each lab group (typically a pair of students) receives two Owaga passive samplers (Figure S2), one for the real sample and one for the blank.Owaga passive samplers are taken and completely disassembled using tweezers, taking care not to mix the parts of both samplers.All the sampler components must be washed with distilled water and dried before each use, except for the collection pads.
Figure S3 shows the complete exploded view of an Owaga sampler.Expose one of the two Owaga samplers to ambient air, noting the exact start time of sampling.The other sampler is kept in a sealed opaque box for the same time (blank).

Procedure for obtaining the calibration curve:
To five 10 mL volumetric flasks, add increasing volumes of the 20 mg L -1 ITS working standard, so that the final volume of the flask contains ITS concentrations between 1 and 20 mg L -1 , and add water to the mark (Table S1).Record absorbances at 600 nm, using distilled water as a blank.

Measurement of real and blank samples:
Remove the samplers from their places of exposure to the ambient air, noting the exact time of the end of the collection.Dismantle the samplers with tweezers by removing the two pads and placing them together in a 10 mL flask containing about 7 mL of distilled water.Sonicate the flask, make up to the mark with distilled water and measure the absorbance.Repeat the procedure with the sampler used as blank.Record the absorbance As (sample) and Ab (blank).

3.RESULTS
-Graph the calibration curve.Adjust it by the least squares method and check its quality parameters.
-Calculate the concentration of ITS in the real sample (Cs) and the blank (Cb).
-Calculate the ozone mass in micrograms equivalent to the mass of ITS consumed, according to the stoichiometry of the reaction in Figure S1.
-Calculate the ozone concentration in the ambient air according to Eq. S8, considering that the sampling rate for the Ogawa samplers is 21.8 x 10 -6 m 3 min -1 (manufacturer's data).
-Calculate the relative standard deviation of the determination, using the set of experimental data obtained in the experimental session.
-Calculate the accuracy of the determination as relative error with respect to the certified value of ozone concentration measured in the air quality monitoring station of Badajoz, belonging to the REPICA network (Red Extremeña de Protección e Investigación de la Calidad del Aire).The instructors will provide this data.
-Calculate the relative expanded uncertainty by the validation tool using the experimental data set obtained in the two experimental sessions and the data measured in previous years' courses (Table S2).

Supporting Information
Journal of Chemical Education 11 7. Calculate the ozone concentration in ambient air (µg m -3 ) using Eq.(S8).S is the sampling rate provided by the Ogawa sampler manufacturer (S = 21.8 x 10-6 m 3 min -1 ) and t is the sampling time (min).

SECTION 4. SURVEY
Thank you for reporting your user experience of the Macro Sensor Validation Tool (SVT).
The results will be treated anonymously.This tool has been developed with funding from the European project NanoSenAQM (Interreg-Sudoe programme) and is currently used in the regional project Comunicaire (funded by the Junta de Extremadura) and in other projects of the AQUIMA research group of the UEx.These projects are co-financed by the European Regional Development Fund (ERDF).

SECTION 2 .
HANDOUT PROVIDED TO STUDENT WITH THE LAB EXERCISE DETERMINATION OF OZONE IN AMBIENT AIR BY PASSIVE SAMPLING AND DETECTION BY MOLECULAR ABSORPTION SPECTROPHOTOMETRY (VISIBLE) OBJETIVE Training in the technique of passive sampling and measurement by UV-Vis molecular absorption spectrophotometry to determine the levels of atmospheric pollutants in ambient air.1.INTRODUCTION Tropospheric ozone is a secondary pollutant formed by photochemical reactions of volatile organic compounds (VOCs) and nitrogen oxides (NOx) activated by solar radiation and temperature.In southern Europe and other climatic regions with similar characteristics, tropospheric ozone is a major environmental problem.Continuous exposure to high concentrations of ozone in ambient air can cause damage to public health and vegetation.Current European environmental legislation sets different maximum levels for ambient concentrations of tropospheric ozone for the protection of human health and ecosystems.Different analytical methodologies have been developed to determine ozone levels in ambient air.The standard methodology commonly used in air quality monitoring networks is based on measuring ozone absorbance in the ultraviolet region by a continuous analyzer provided with a suction pump for air sampling (standard UNE-EN 14625/2013).It is a reliable method, although the equipment required is expensive to purchase and maintain.However, there is a more affordable alternative based on passive sampling in which ozone migrate by diffusion to a membrane impregnated with indigo trisulfonate (ITS), where the reaction shown in Figure S1 occurs.

Figure S1 .
Figure S1.Reaction of ITS with ozone.
mg L -1 ITS stock solution, in distilled water:ethylene glycol (50:50).The appropriated amount of the reagent is added to a 25 mL flask containing 12.5 mL ethylene glycol and made up to the final volume with distilled water.Store away from light.

Figure S3 .
Figure S3.Complete exploded view of an Owaga sampler.

Q1.
In your opinion, how useful is the validation tool? I do not see any benefit  It has been of little benefit to me  I find it quite useful Q2.What is your opinion on the instructions provided by the validation tool? I did not understand the instructions  I have partially understood the instructions  I have understood all the instructions Q3.In your opinion, how user-friendly is the validation tool?not understand what the results mean  I partially understood what the results mean  I perfectly understood what the results mean

Table S2 . Experimental data set measured in previous years' courses.
-Compare the experimental ozone concentration value measured with the limit values contemplated in the air quality legislation (Real Decreto 102/2011).